We measure the magnitude and phase of both independent components of the femtosecond (fs) third-order nonlinear optical susceptibility tensor (chi) (3)(-(omega) ;(omega) ,(omega) ,-(omega) ) of a C60 film. We observe only the contribution of mechanisms whose rise and decay times are short compared to our 120 fs microjoule pulses. The value of (chi) 1111 varies between (6.39 +/- 0.35) X 10-13 esu at 745 nm and (19.7 +/- 1.1) X 10-13 esu at 875 nm, relative to fused silica, and rises monotonically with wavelength. Its phase angles lie between 100 and 150 degrees. Our results indicate that neither our, nor any previously published, measurements can be assumed to have approached the low frequency limit in C60.